Question

7. A car weighing 1500 kg moving with a velocity of 72 km/h retards uniformly to rest in 20 s. Find the change in momentum takes place in 1 s.

Answer 1

Answer:

change in momentum =mv - mu =  m(v-u)

we know v-u = at , so change in momentum = m (at) - (1)

Explanation:

to find acceleration

initial velocity = 72 x 5/18 = 20m/s

given that the comes to rest in 20 s

so final velocity = 0 , time [t] = 20 s

v-u = at

0-20 = a x 20

- 20/20 = a

=> a = -1 , substitute a = -1 in equation - (1)

then change in momentum = 1500 ( -1 x t )

given they asked to find change in momentum for 1 s , so t = 1 s

change in momentum = 1500 ( -1 ) = -1500

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Change\:in\:momentum=-1500\:kg\:m/s}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Mass \: of \: car = 1500 \: kg \\ \\ \tt: \implies Initial \: velocity = 72 \: km/h \\ \\ \tt: \implies Time \: taken \: to \: be \: in \: rest = 20 \: s \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Change \: in \: mometum \: after \: 1 \: sec =?$

• According to given question :

$\tt \circ \: Initial \: veocity = 72 \times \frac{5}{18} = 20 \: m/s \\ \\ \tt \circ \: Final \: velocity = 0 \: m/s \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies 0 = 20 + a \times 20 \\ \\ \tt: \implies - 20 = 20 \times a \\ \\ \tt: \implies a = \frac{ - 20}{20} \\ \\ \green{\tt: \implies a = - 1 \: m /{s}^{2} } \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v_{f} = u + a t_{1} \\ \\ \tt: \implies v_{f} = 20+ ( - 1) \times 1 \\ \\ \tt: \implies v_{f} =20 - 1 \\ \\ \green{\tt: \implies v_{f} = 19 \: m/s} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Change \: in \: momentum = m \Delta v \\ \\ \tt: \implies Change \: in \: momentum = m( v_{f} - v_{i}) \\ \\ \tt: \implies Change \: in \: momentum =1500(19 - 20) \\ \\ \tt: \implies Change \: in \: momentum =1500 \times ( - 1) \\ \\ \green{\tt: \implies Change \: in \: momentum = - 1500 \: kg \: m/s}$